FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 3, PAGES 61-66

Every zero adequate ring is an exchange ring

B. V. Zabavsky
S. I. Bilavska

Abstract

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It is proved that if $R$ is a commutative ring in which zero is an adequate element, then $R$ is an exchange ring and that every zero adequate ring is an exchange ring. There is a new description of adequate rings; this is an answer to questions formulated by Larsen, Lewis, and Shores.

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Last modified: May 4, 2012